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NEET 2023

Exam: NEET
Year: 2023
Subject: Physics
Chapter: Ray Optics

NEET 2023 · Physics · Ray Optics

Light travels a distance x in time t _ 1 in air and 10x in time t _...

Light travels a distance

x

in time

{t}_{1}

in air and

10x

in time

{t}_{2}

in another denser medium. What is the critical angle for this medium?

Options

A $\sin^{- 1} ( \dfrac{10{t}_{1}}{{t}_{2}} )$
B $\sin^{- 1}\left(\dfrac{{t}_{2}}{{t}_{1}}\right)$
C $\sin^{- 1}\left(\dfrac{10{t}_{2}}{{t}_{1}}\right)$
D $\sin^{- 1}\left(\dfrac{{t}_{1}}{10{t}_{2}}\right)$

Correct answer

A. $\sin^{- 1} ( \dfrac{10{t}_{1}}{{t}_{2}} )$

Step-by-step solution

Applying Snell's law for refraction from denser to rarer medium, we get
${μ}_{denser} \timessinC = {μ}_{air} \timessin90 ° ⇒\dfrac{c}{vdenser}$ s $inC =\dfrac{c}{vair}\times1 ⇒ \dfrac{c}{\dfrac{10x}{t2}}sinC = \dfrac{c}{\dfrac{x}{t1}}⇒ sinC = \dfrac{10{t}_{1}}{t2}⇒ C = \sin^{- 1} \left(\dfrac{10{t}_{1}}{t2}\right)</p></blockquote>$

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